Coupled task problem on a single machine consists of scheduling a set of jobs, where each job has two tasks. These tasks have to be scheduled so that no tasks overlap and the two tasks of a job are scheduled with exactly their given delay time in between them. We focus on the minimization of the total completion time of the jobs. Recently, [1] drew an almost full complexity picture for these problems. In this talk, we will present approximation algorithms for several NP-hard variants based on the results of [2]. Acknowledgements: This research has been supported by the TKP2021-NKTA-01 NRDIO grant on ”Research on cooperative production and logistics systems to support a competitive and sustainable economy”.